Father Kenneth Walker, 28, was shot and killed in the attack. Father Joseph Terra, 56, is in critical but stable condition after being beaten, according to police.

The priests were attacked in the church's living quarters, apart from the sanctuary.

"It was a bad scene," said police sergeant Steve Martos. "We're just not that sure what the motive is in this one," he said.

"We are stunned and deeply saddened to learn of the tragic assault perpetrated last night against [Father Terra] and [Father Walker], two religious order priests who belong to the Priestly Fraternity of St Peter," said a statement released by the Diocese of Phoenix.

Though the attack was reported to police as a burglary, Martos said he was uncertain whether theft motivated the attack. Police found a missing charcoal Mazda Tribute owned by one of the priests a few blocks away, but it's unclear if anything else is missing from the residence.

"It's difficult to kind of put your head around who would do or why they would do it," said Martos. "First, you're talking about the location – a church... Then, the victims, the specific victims who were attacked, and obviously the severity of the injuries."